Average Error: 0.4 → 0.1
Time: 2.5m
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{1}{\frac{\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)}}{\frac{\frac{1 - v \cdot \left(5 \cdot v\right)}{1 - v \cdot v}}{\pi}}}}{t}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{\frac{1}{\frac{\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)}}{\frac{\frac{1 - v \cdot \left(5 \cdot v\right)}{1 - v \cdot v}}{\pi}}}}{t}
double f(double v, double t) {
        double r555712 = 1.0;
        double r555713 = 5.0;
        double r555714 = v;
        double r555715 = r555714 * r555714;
        double r555716 = r555713 * r555715;
        double r555717 = r555712 - r555716;
        double r555718 = atan2(1.0, 0.0);
        double r555719 = t;
        double r555720 = r555718 * r555719;
        double r555721 = 2.0;
        double r555722 = 3.0;
        double r555723 = r555722 * r555715;
        double r555724 = r555712 - r555723;
        double r555725 = r555721 * r555724;
        double r555726 = sqrt(r555725);
        double r555727 = r555720 * r555726;
        double r555728 = r555712 - r555715;
        double r555729 = r555727 * r555728;
        double r555730 = r555717 / r555729;
        return r555730;
}
↓
double f(double v, double t) {
        double r555731 = 1.0;
        double r555732 = 2.0;
        double r555733 = 1.0;
        double r555734 = v;
        double r555735 = 3.0;
        double r555736 = r555734 * r555735;
        double r555737 = r555734 * r555736;
        double r555738 = r555733 - r555737;
        double r555739 = r555732 * r555738;
        double r555740 = sqrt(r555739);
        double r555741 = 5.0;
        double r555742 = r555741 * r555734;
        double r555743 = r555734 * r555742;
        double r555744 = r555733 - r555743;
        double r555745 = r555734 * r555734;
        double r555746 = r555733 - r555745;
        double r555747 = r555744 / r555746;
        double r555748 = atan2(1.0, 0.0);
        double r555749 = r555747 / r555748;
        double r555750 = r555740 / r555749;
        double r555751 = r555731 / r555750;
        double r555752 = t;
        double r555753 = r555751 / r555752;
        return r555753;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{t \cdot \pi}}{\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)}}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.4

    \[\leadsto \frac{\frac{\color{blue}{1 \cdot \frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}}{t \cdot \pi}}{\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)}}\]

  5. Applied times-frac0.4

    \[\leadsto \frac{\color{blue}{\frac{1}{t} \cdot \frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}}{\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)}}\]

  6. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{t}}{\frac{\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)}}{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{1 - v \cdot v}}{\pi}}}}\]

  7. Simplified0.3

    \[\leadsto \frac{\frac{1}{t}}{\color{blue}{\frac{\sqrt{2 \cdot \left(1 - \left(v \cdot 3\right) \cdot v\right)}}{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{1 - {v}^{2}}}{\pi}}}}\]
  8. Using strategy rm

  9. Applied div-inv0.3

    \[\leadsto \color{blue}{\frac{1}{t} \cdot \frac{1}{\frac{\sqrt{2 \cdot \left(1 - \left(v \cdot 3\right) \cdot v\right)}}{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{1 - {v}^{2}}}{\pi}}}}\]
  10. Using strategy rm

  11. Applied associate-*l/0.1

    \[\leadsto \color{blue}{\frac{1 \cdot \frac{1}{\frac{\sqrt{2 \cdot \left(1 - \left(v \cdot 3\right) \cdot v\right)}}{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{1 - {v}^{2}}}{\pi}}}}{t}}\]

  12. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{1}{\frac{\sqrt{2 \cdot \left(1 - v \cdot \left(3 \cdot v\right)\right)}}{\frac{\frac{1 - v \cdot \left(v \cdot 5\right)}{1 - v \cdot v}}{\pi}}}}}{t}\]

  13. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{\sqrt{2 \cdot \left(1 - v \cdot \left(v \cdot 3\right)\right)}}{\frac{\frac{1 - v \cdot \left(5 \cdot v\right)}{1 - v \cdot v}}{\pi}}}}{t}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))